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Proof step 27 from proof inv-inverts (previous step)

max∞(λ n0. nσ[n0] = nσ[n]) = ⌜n⌝ , # nσ = ∞, nσ[n + 1] = nσ[n] + 1, n ≤ m, stutf(nσ), ∀ m0. m < m0 → nσ[m0] = nσ[m] + 1, ¬ n < m → nσ[n] = nσ[m] ⊦ ((λ m0. max∞(λ n0. nσ[n0] = m0).n) to nσ[m] + 1)[nσ[n]] = n

User applied rule cut formula

And obtained the following new goals

Proof step 28:
n < m, max∞(λ n0. nσ[n0] = nσ[n]) = ⌜n⌝ , # nσ = ∞, nσ[n + 1] = nσ[n] + 1, n ≤ m, stutf(nσ), ∀ m0. m < m0 → nσ[m0] = nσ[m] + 1, ¬ n < m → nσ[n] = nσ[m] ⊦ ((λ m0. max∞(λ n0. nσ[n0] = m0).n) to nσ[m] + 1)[nσ[n]] = n

Rule argument

fma: n < m

Additional information

Used simplifier rules: lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%anti: ⊦ m ≤ n → (n ≤ m ↔ m = n); from specification nat%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%get-infto: m < n ⊦ (nnf to n)[m] = nnf(m); from specification stream[natstream]%sel: ⊦ ⌜m⌝ .n = m; from specification nat-inf-basic Used formulas: n < m